The notions of closedness and D-connectedness in quantale-valued approach spaces

Abstract

In this paper, we characterize local $T_{0}$ and $T_{1}$ quantale-valued gauge spaces, show how these concepts are related to each other and apply them to $mathcal{L}$-approach distance spaces and $mathcal{L}$-approach system spaces. Furthermore, we give the characterization of a closed point and $D$-connectedness in quantale-valued gauge spaces. Finally, we compare all these concepts to each other.

Keywords

• $mathcal{l}$-approach distance space
• $mathcal{l}$-gauge space
• topological category
• separation
• closedness
• d-connectedness